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AN  ANGULAR  TOUR  OF  THE  WORLD 

OR 

THE  CURIOSITIES 

OF 

Latitude  and  Longitude 

A  BOOK  FOR  TEACHERS 


BY 

EDWARD  R.  E.  COWELL 
Member  of  the  Chicago  Academy  of  Sciences 


PUBLISHED  BY 

THOMAS   CHARLES  CO 
CHICAGO 


COPYRIGHTED  1894 

BY 
E.  R.  E.  COWELL 


Engineering  $ 
Mathematical 
Sciences  &  3  / 

"*">       C33 


TO   THE   TEACHER. 

^  I  AHE  object  of  this  little  work  is  to  make  the  sub- 
•A.  ject  clear,  so  that  it  may  be  intelligently  pre- 
sented to  your  classes.  A  clear  understanding  of  the 
earth's  motions  and  the  relation  of  the  earth  to  the 
other  heavenly  bodies  is  necessary  in  teaching  mathe- 
matical geography. 

Facts  belong  to  the  physical  world  and  truths  to 
the  moral  and  spiritual  world.  A  teacher  who  has 
the  best  and  highest  development  of  the  scholar  in 
view  will  combine  facts  and  truths  in  teaching. 

L/et  me  explain.  ' '  The  world  rotates  on  its  axis 
once  in  twenty-four  hours."  That  is  a  physical  fact. 
' '  We  must  always  have  a  cause  adequate  to  produce 
an  effect."  That  is  a  moral  truth.  "The  earth's 
axis  is  inclined  sixty-six  and  one-half  degrees  to  the 
sun's  path."  That  is  a  fact.  " The  wisdom  of  this 
arrangement  is  evident. ' '  That  is  a  truth. 

I  believe  in  the  concrete  idea  in  teaching.  In 
order  to  present  a  fact  so  that  it  may  be  readily  seen, 
it  should  be  given  in  a  concrete  form.  I  believe  the 


4  TO   THE   TEACHER. 

truth  can  be  arrived  at  without  wasting  the  mental 
powers  in  mere  mathematical  gymnastics. 

We  must  understand  the  principles  involved  in  a 
problem,  get  a  bird's-eye  view  of  it,  get  down  to  the 
roots  of  it  and  out  to  the  twigs  of  it — grasp  it.  It  is 
of  no  use  to  work  out  a  problem  by  rule  unless  the 
student  understands  the  reason  for  the  rule. 

I  believe  in  fulness  of  explanation  and  in  variety 
of  illustration,  and  in  arriving  at  knowledge  by 
inductive  reasoning;  and  let  us  forever  bear  in  mind 
this  truth,  that  "  we  must  always  have  a  cause  ade- 
quate to  produce  an  effect. ' ' 


STATE  NORMAL  SCHOOL, 

ItOS  AfiCEIlES,  GRU. 


CONTENTS. 

PAGK. 

Accurate  Clocks 45 

Altitude , .,... 25 

Angle  of  Night  Shadow 28 

Angular  Distances 41 

Angular  Tour  of  the  World.  ., 10 

Antipodal  Meridian 20-5(5 

Antipodes 20 

Apparent  Sun  Time 64 

Apparition ... 18 

Astronomical  Geography & 

A  Wonderful  Clock 45 

Axis  of  Rotation 14 

Belts  (Zone) 15 

Beginning  of  a  Day • 51 

Celestial  Pole 36 

Center  of  Gravity 34 

Changes  in  Appearance  of  the  Heavens  37 

Circumnavigating  the  Globe 60 

Climate 22 

Clocks  Agree 21 

Clocks  Differ 21 

Clock— The  Earth 42-44 

Co-Latitude 25 

Co-Incident  Phenomena  :'>-J 

Compensation  Balance 30 

Concentric    Zone  Boundaries....  ..   14 


0  CONTENTS. 

Concrete  Teaching 3 

Cone  of  Rotation 43 

Date  Line 53 

Dawn  and  Twilight 36 

Day 42 

Declination 25 

Direction  of  Rotation  and  Revolution.    ...  13 

Diurnal  Rotation 34 

East  and  West 35 

Equator 39 

Equinoxes 12 

Facts  and  Truths 3 

Gain  or  Loss  of  Time; 57 

Gravity 39 

Greenland   17 

Greenwich  Mean  Time 63 

Gyroscope  43 

Heat „ 31 

Inclination  of  Axis 12 

International  Date  Line 53 

Land  of  the  Midnight  Sun 17 

Latitude  and  the  Sun's  Meridian  Altitude 23 

Defined 33 

How  to  Obtain 26 

Of  Cities 76 

Law  of  Compensation 30 

London 51 

Longest  Day 18 

Longitude  Defined 41 

How  Obtained  at  Sea 63 

Of  Cities....  76 


CONTENTS.  7 

Longitude— Proof  of  Earth's  Rotundity '. 10 

'Longitudinal  Quadrants  of  the  Earth 54 

Magnetic  Pole 34 

Making  of  a  Zone 13 

Mathematical  Geography 40 

Mean  Sun  Titne 65 

Meridian  180 53 

Meridians 41 

Midnight 56 

Motions  of  a  Steam  Engine 11 

Mountain-top  Temperatures   22 

Night 23 

Night  Shadow 19-30 

Noon 22 

North  Polar  Star  33 

Norway 17 

Occupation 18 

Parallels 15 

Parallelism  of  the  Axis 12 

Pendulum , 39 

Phenomena  of  Day  and  Night 29 

Place  of  Sun's  Rising  and  Setting 28 

Polaris 43 

Poles 36 

Precession  43 

Proofs  of  Earth's  Rotundity 10 

Revolution 13 

Rising  and  Setting  Stars 39 

Rotation 13 

Sidereal  Time 44 

Sidereal  Clock....  ..    44 


8  CONTENTS. 

Sea  Level  Temperatures .    22 

Seasons. 1* 

Sextant 64 

Shape  of  the  Earth 32-72 

Standard  Time 67 

Succession  of  Days 49 

Sun's  Declination 19 

Sun's  Meridian  Altitude 23 

Sun-DialTime 23 

Telegrams  from  Distant  Points ...  10 

The  Midnight  Sun 17 

Time .". 42 

Value  of  a  Degree — 

Latitude 72 

Longitude 70 

Watches ., 45 

Where  does  the  Day  Begin? .'.,  51 

Width  of  the  Zones 15 

Yesterday  and  Today 55 

Zones — How  Made t 18 

ILLUSTRATIONS. 

1.— The  Earth 6ti 

2. — Rotation  of  the  Northern  Heavens 35 

3.— Twilight  Projection 37 

4.— The  Hour  Angle 47 

5. — Longitudinal  Quadrants 54 

6.— Direction  of  Rotation,  etc 13 

7.— Sunrise  and  Sunset  Points .'. 28 

8. — Sun's  Meridian  Altitude 24 

9.— Angle  of  the  Sun's  Rays ...  25 


AN  ANGULAR  TOUR  OF  THE  WORLD; 


The  Curiosities  of  Latitude  and  Longitude 

LATITUDE BREADTH. 

LONGITUDE...  ...LENGTH. 


HT^HERE  is  no  latitude  at  the  equator  and  no  longi- 
-*•  tude  at  London  (or  Greenwich),  these  being  the 
initial  or  starting-points  from  which  latitude  and 
longitude  are  measured.  We  may  define  the  position 
of  any  place  on  the  earth  very  accurately  by  giving 
its  latitude  and  longitude. 

The  City  Hall.  New  York,  for  instance,  is  40°  42' 
44"  north  latitude  and  74°  o'  24"  west  longitude. 

Yale  College,  New  Haven,  is  41°  18'  28"  north 
latitude  and  72°  55'  45"  west  longitude. 

The  State  House,  Boston,  is  42°  21'  28"  north 
latitude  and  71°  3'  50"  west  longitude. 

The  Auditorium,  Chicago,  1541°  53'  north  latitude 
and  87°  37'  west  longitude. 


10       CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

One  of  the  simplest  and  most  self-evident  proofs 
of  the  rotundity  or  sphericity  of  our  earth  is  in  con- 
nection with  longitude. 

If  the  earth  were  flat,  the  sun  at  rising  would 
appear  at  the  same  instant  to  every  one  west  of  it,  say 
at  Yokohama,  Athens,  London,  New  York,  Chicago 
and  San  Francisco. 

Now  the  fact  is,  that  when  the  sun  is  rising  in 
Australia  it  is  setting  in  England,  and  it  is  on  the 
meridian  of  (or  noon  at)  Chicago,  all  at  the  same 
instant. 

If  we  were  to  send  a  telegram  from  Melbourne  in 
the  early  morning  (sunrise)  of  Sunday,  July  i,  it 
would  reach  Chicago  Saturday  noon,  June  30,  the 
previous  day. 

L/et  me  take  you  on  a  personally  conducted  tour 
around  the  world.  We  will  travel  around  the  earth 
obliquely,  at  an  angle  of  66^  degrees  to  the  equator, 
crossing  every  meridian  and  every  parallel  as  far  as 
the  two  circles.  This  might  be  called  "An  Angular 
Tour  of  the  World. ' '  We  shall  witness  some  very 
interesting  phenomena. 

The  curiosities  of  latitude  and  longitude  are  simply 
those  phenomena  we  experience  by  change  of  posi- 
tion. If  a  person  living  on  the  equator  and  used  to 
seeing  the  sun  rise  and  set  at  six  o'clock  every  day 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       II 

throughout  the  year  were  to  go  to  latitude  66^3  north 
(on  June  21),  he  would  see  the  sun  at  midnight.  This 
to  him  would  be  a  curiosity;  it  is  a  phenomenon  of 
latitude. 

Suppose  a  person  living,  say,  at  San  Francisco, 
saw  the  sun  set  at  5  p.  M.,  and  could  travel  rapidly 
around  the  earth  on  that  parallel,  the  sun  would  set 
at  5  P.  M.  for  him  at  Pekin,  China,  and  every  other 
place  on  the  parallel,  provided  he  had  adjusted  his 
watch  to  the  local  time  of  the  place.  That  is  a  phe- 
nomenon of  longitude  and  latitude. 

Now,  suppose  a  person  lived  at  the  Arctic  Circle, 
on,  say,  meridian  75  west  longitude,  another  at  the 
Equator,  and  another  at  the  Antarctic  Circle,  on  the 
same  meridian  ;  all  three  would  have  exactly  the 
same  time — their  clocks  would  all  agree. 

L/et  me  give  you  an  analysis  of  the  strange  and 
complex  phenomena  which  I  call  the  "  Curiosities  of 
Latitude  and  Longitude.''  Three  causes  combine  to 
produce  these  results: 

First — The  axial  rotation  of  the  earth  (diurnal). 

Second — The  inclination  of  the  axis  of  rotation. 

Third — The  earth's  yearly  revolution  around  the 
sun. 

Did  you  ever  watch  the  motions  of  the  separate 
parts  of  a  steam  engine — valve,  piston  and  valve- 


12       CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

gear?  The  motion  of  each  is  simple;  each  part 
works  in  harmony  with,  and  in  relation  to,  the  other 
parts;  the  result  looks  complex.  Just  so  in  regard  to 
the  several  motions  of  the  earth. 

Note,  now,  the  effect  of  the  inclination  of  the 
earth's  axis,  66^  degrees,  to  the  plane  of  its  orbit, 
or  23^*  to  a  perpendicular  to  the  plane  of  the  earth's 
orbit.  The  equator  is  inclined  23  ^  degrees  to  the 
apparent  path  of  the  sun,  or  the  ecliptic.  The  par- 
'allelism  of  the  axis  to  itself  in  the  yearly  journey  is 
strictly  maintained. 

The  rotation  of  the  seasons  —  spring,  summer, 
autumn  and  winter  —  is  one  result  of  this  inclina- 
tion, and  the  belting  of  the  earth  with  zones  is 
another. 

In  the  rotation  of  seasons  it  will  be  observed  that 
in  both  spring  and  fall  (or  autumn)  seasons  days  and 
nights  are  equal\  all  over  the  globe.  The  night 
shadow  is  then  perpendicular,  whereas  in  the  summer 
and  winter  seasons  the  greatest  possible  variation 
takes  place  in  the  length  of  day  and  night  and  in  the 
'  position  of  the  night  shadow. 

The  plane  of  the  ecliptic,  or  sun's  path,  is  the 
the  plane  of  the  earth's  orbit.  This  crosses  the 
equator  at  an  angle  of 


*  23°-28/.    f  Equinox—  Vernal  March  21,  and  Autumnal  Sept.  21  . 


CURIOSITIE 


ES  OF  LA 


TITUDE  AND  LONGITUDE.       13 


The  inclination  of  the  axis  to  the  plane  of  the 
earth's  orbit  is  66^°  or  23^°  to  a  perpendicular  to 
the  plane.  The  following  diagram  shows  the  direc- 
tion of  revolution  and  rotation,  also  the  fixed  axis  of 
rotation : 


ZONES— HOW  MADE. 

What  makes  a  zone  ? 

Did  you  ever  watch  a  wood-turner  at  his  lathe? 
Let  him  touch  any  point  on  a  revolving  cylinder  or 
globe  with  the  point  of  his  instrument  and  instantly 
that  point  becomes  a  circle  by  the  rotation  of  the 
cylinder  on  its  axis,  and  the  fixed  position  of  the  axis. 

Now,  if  the  rays  of  the  sun  touch  a  point  north  or 
south,  say,  for  instance,  the  Arctic  Circle,  the  diurnal 


14       CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

rotation  of  our  globe  makes  that  point  a  circle.  As 
compared  to  the  (apparent)  moving  sun  in  his  yearly 
path,  the  earth's  rotation  is  rapid. 

Here  is  another  point,  say  23°  28'  nortri  of  the 
equator,  over  which  the  sun  is  vertical;  the  daily 
rotation  makes  this  a  circle  again,  and  that  circle  is 
the  Tropic  of  Cancer.  Now,  if  the  sun  is  vertical  (in 
the  zenith)  at  any  point  on  the  Tropic  of  Cancer,  he 
is  vertical  at  every  point  on  that  parallel;  for  the  time 
being  the  "sun  stands  still,"  while  the  earth  keeps 
on  rotating,  and,  as  the  Tropic  of  Cancer  is  the  limit 
of  the  sun's  path  north  of  the  equator,  of  course  it  is 
the  limit  of  verticality,  hence  marks  the  northern 
boundary  of  the  Torrid  Zone. 

Observe  that  these  circles  are  all  concentric,  paral- 
lel to  each  other,  because  of  the  fixed  position  of  the 
axis  of  rotation.  No  matter  how  many  points  may 
be  touched  by  the  wood-turner  in  his  work,  these 
all  become  concentric  circles,  because  of  the  fixed  axis 
of  rotation. 

This  explains  why  the  same  series  of  phenomena 
takes  place  at  all  points  "on  a  parallel.  It  is  due  to 
the  stationary  sun  (for  the  time)  and  the  rapidly 
rotating  earth.  Were  the  rotation  slower  (say  a 
month),  there  would  be  quite  an  appreciable  difference 
in  the  phenomena  at  different  places  on, a  parallel. 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       15 

A  parallel  is  a  circle  running  around  the  earth,  east 
and  west,  smaller  than  the  equator,  all  points  of 
which  are  equally  distant  from  the  equator.  It  is  a 
circle  parallel  to  the  equator. 

From  what  has  been  said,  it  will  readily  be  seen 
that  the  zones  are  made  practically  by  the  sun, 
in  combination  with  the  rotating  earth  and  the  fixed 
axis  of  rotation. 

There  are  five  zones,  as  there  are  five  races  of  men, 
and  five  great  continents  and  five  large  oceans.  As 
the  Arctic  and  Antarctic,  or  Frigid  Zones,  bound  the 
limit  of  the  sun's  rays  at  the  winter  solstice,  so  the 
Torrid  Zone  bounds  the  limit  of  his  verticality  at  the 
summer  solstice. 

The  width  of  the  zones,  therefore,  corresponds 
with  the  apparent  movements  of  the  sun,  the  inclina- 
tion of  the  earth's  axis  to  a  perpendicular  to  the 
ecliptic,  or  sun's  path,  being  23  degrees  and  28  min- 
utes. So  we  have  the  widths  of  the  zones  as  follows: 

Arctic 23°  28' 

North  Temperate 43°  04' 

Torrid 46°  56',  or  twice  23°  28' 

South  Temperate 43°  04' 

Antarctic 23°  28' 

1 80°  oo' 


1 6       CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

It  will  be  observed  by  this  arrangement  that  the 
greatest  possible  width  is  given  to  that  portion  of  the 
earth  best  adapted  to  man  and  his  needs,  /.  e. ,  best 
adapted  for  his  occupation,  namely,  the  two  temperate 
s  zones — a  belt  86°  8'  wide,  or  nearly  half  of  the  total 
of  1 80  degrees. 

The  proportion  is  very  much  larger  than  this  when 
we  consider  the  area  of  this  belt.  The  value  of  a 
degree  of  longitude  rapidly  diminishes  as  we  approach 
the  poles — so  that  the  area  of  the  Frigid  Zones  is  much 
smaller  in  proportion  to  their  width  than  the  Temper- 
ate or  Torrid  Zones. 

If  the  earth's  equator  were  not  inclined  23°  28'  to 
the  ecliptic  or  sun's  path,  that  is,  if  the  sun  moved 
in  the  equator  instead  of  the  ecliptic,  eternal  cold 
and  darkness  would  prevail  at  some  places,  and  eter- 
nal heat  and  light  at  others.  It  is  the  inclination  of 
the  axis  plus  the  rotation  of  that  axis,  together  with 
the  yearly  path  of  the  sun,  that  produces  the  compen- 
satory balance  of  the  alternate  and  equal  distribution  of 
heat  and  cold,  light  and  darkness  for  the  whole  earth. 
I  believe  the  earth  is  adapted  to  man  and  his  needs. 
The  wisdom  of  the  inclination,  rotation  and  revolution 
is  evident;  nothing  in  Nature  is  accidental.  When 
the  "  Heavens  and  the  Earth  were  finished"  they  were 
finished  in  the  sense  of  perfection  and  completeness. 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       IJ 

Suppose  the  axis  of  the  earth  were  inclined  56^° 
instead  of  66 y>  °  to  the  plane  of  its  orbit.  New  Orleans 
would  then  be  in  the  Torrid  Zone,  and  Edinburgh 
would  be  in  the  Arctic  Zone. 

Suppose  the  inclination  were  76^°,  Greenland 
would  then  be  in  the  North  Temperate  Zone,  and 
Bombay,  which  is  now  in  the  Torrid,  would  be  in  the 
North  Temperate  Zone. 

Now  suppose  the  angle  of  the  ecliptic  to  the  equa- 
tor was  30°  instead  of  23°  28'.  The  width  of  the 
zones  would  be  as  follows:  Torrid,  60°;  the  two  Frigid 
Zones,  30°  each;  the  Temperate  Zones,  30°  each, 
and  England  would  then  be  in  the  Arctic  Zone  and  in 
winter  would  have  no  sun  at  all. 

Travelers  call  Norway  the  land  of  the  midnight 
sun,  but  this  is  true  of  any  land  beyond  the  665^  par- 
allel of  latitude.  On  the  2ist  of  June  the  sun  does 
not  set  at  all  from  the  Arctic  Circle  to  the  North  Pole, 
and  on  the  2ist  of  December  he  does  not  set  from  the 
Antarctic  Circle  to  the  South  Pole. 

I  suppose  that  the  reason  why  Norway  is  especially 
designated  as  the  "  Land  of  the  Midnight  Sun"  is, 
that  Norway  is  accessible  to  travelers  and  is  in  the 
regular  route  of  excursion  travel,  but  Greenland, 
being  within  the  Arctic  regions,  is  getting  to 
be  quite  as  accessible,  and  is  just  as  much  the 


1 8       CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

"Land  of  the  Midnight  Sun"  as  are  Sweden  and 
Norway. 

The  two  polar  circles  are  the  farthest  limits  north 
and  south  where  a  day  can  consist  of  just  twenty-four 
hours  (on  June  21  and  December  21)  with  no  night. 
Less  than  these  two  points  the  day  can  never  be 
twenty-four  hours  long.  Beyond  these  circles  the  day 
may  be  anywhere  from  24  hours  to  six  months  long. 
The  two  circles,  therefore,  mark  the  maximum  twenty- 
four-hour  day,  or  a  period  of  twenty-four  hours  when 
the  sun  is  above  the  horizon. 

Let  me  explain  this  phenomenon  of  latitude. 

The  greatest  length  of  the  day  for  all  latitudes 
north  of  the  equator,  occurs  on  June  21.  The  night 
shadow  then  extends  in  a  diagonal  line  from  one  edge 
of  the  Arctic  Circle,  to  the  opposite  edge  of  the  Ant- 
arctic Circle,  thus  uncovering  (or  exposing  to  the  sun's 
rays)  the  northern  Frigid  Zone,  and  completely  cov- 
ering the  southern.  The  cut  on  page  28  shows  the 
position  of  the  night  shadow  for  June  21.  This 
diagonal  line  cuts  the  equator  at  an  angle  of  66  ]/2  ° 
and  is  23}^°  from  the  meridian  or  perpendicular. 

At  the  equator  the  day  would  be  just  12  hours 
long,  the  sun  would  rise  at  6  and  set  at  6;  at  the  55th 
parallel  the  day  would  be  18  hours  long;  sun  rises  at 
3  and  sets  at  9;  at  the  66 ^<  parallel,  the  day  is  24 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       19 

hours  long  and  the  sun  neither  rises  nor  sets,  but  at 
noon  he  is  47°  high  and  at  midnight  on  the  horizon, 
and  due  north.  At  the  55th  parallel  south,  the  day 
would  be  now,  only  six  hours  long;  sun  rises  at  9  and 
sets  at  3.  At  the  66^4  parallel  south,  there  would 
be  no  day;  sun  does  not  rise  at  all.  The  night  is  24 
hours  long. 

Now  as  the  line  of  the  night  shadow  forms  an  angle 
with  the  meridian,  equal  to  the  angle  of  the  sun  with 
the  equator,  the  greater  the  angle  the  greater  will  be 
the  difference  in  lengths  of  the  day  and  night  at  vari- 
ous latitudes,  and,  as  the  greatest  angle  is  23^°  and 
the  greatest  difference  12  hours  (at  the  Polar  Circles) 
each  degree  would  represent  about  30  minutes.  If, 
therefore,  the  sun  were  4°  north  declination,  there 
would  be  a  difference  of  about  two  hours  between  the 
length  of  the  day  at  the  equator  and  at  the  Polar  Cir- 
cles; that  is,  the  day  would  be  two  hours  in  excess  of 
12  at  the  Arctic  Circle,  and  two  hours  less  than  12  at 
the  Antarctic  Circle.  Four  degrees  south  declination 
would  reverse  this.  Of  course,  at  the  very  poles 
themselves  a  very  slight  angle  would  produce  a  day  of 
24  hours  long  and  as  the  angle  increased,  the  region 
of  perpetual  sunshine  would  increase  in  the  one  Polar 
Zone  and  correspondingly  decrease  in  the  other. 

People  who  live  on  opposite  sides  of  the  earth,  or 


20       CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

the  Antipodes,  have  opposite  latitudes,  longitudes, 
days,  nights  and  seasons.  The  Antipodal  Meridian 
is  the  one  removed  12  hours  from  your  own — your 
Antipodes,  the  point  on  that  meridian  in  opposite  lat- 
itude to  your  own. 

People  living  in  the  same  longitude  have  the  same 
NOON,  and,  in  fact,  all  hours  of  the  day  alike.  Their 
clocks  will  all  agree,  but  the  times  of  their  sunrise 
and  sunset  depends  on  the  declination  of  the  sun  and 
their  latitude.  People  living  on  the  same  parallel  of 
latitude  have  sunrise  and  sunset  at  the  same  hours  rel- 
atively, but  their  clocks  will  all  differ.  The  relative 
time  of  sunrise,  for  instance,  on  the  42d  parallel, 
would  be  the  same  to  all  places  on  that  parallel, 
although  in  absolute  time  they  might  be  hours  apart. 
Sunrise  would  be  at  about  the  same  hour  to  people 
living  in  Boston,  Albany,  Buffalo,  Chicago,  Omaha> 
Pekin,  Constantinople,  Rome  and  Madrid,  although 
these  places  are  widely  apart  in  absolute  time. 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       21 


CLOCKS    ALL    AGREE.      CLOCKS   ALL  DIFFER. 


\\ 


^      'd    ~ 

j  i. 


A  Parallel  of  Latitude. 

Longitude    is    measured 
on  this  line  east  and  west. 


On  this  line  the  lengths 
of  the  day,  time  of  sunrise 
and  sunset  all  differ  (ex- 
cept twice  a  year). 


The  time  at  any  point  on 
this  line  agrees  with  the 
time  at  any  other  point  If 
it  is  XII  (noon)  at  66}^ 
north,  it  is  XII  (noon)  at 
66^  south. 


On  this  line  the  lengths 
of  the  day  and  time  of  sun- 
rise arid  sunset  are  the 
same  at  all  points, 


On  this  line  time  differs 
at  every  point.  No  two 
points  have  the  same  time, 
but  the  relative  time  of 
sunrise  and  sunset  would 
be  the  same  at  every  point. 


I  have  stated  that  all  places  in  the  same  latitude 
have  the  same  seasons,  length  of  day  and  night, 
hours  of  sunrise  and  sunset,  etc.,  but  they  may  not 
have  the  same  climatic  conditions,  on  account  of 


22       CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

various  physical  causes,  mountain  ranges,  ocean  cur- 
rents, etc.  For  instance,  England  and  Labrador  are 
nearly  in  the  same  latitude,  but  the  equatorial  cur- 
rents that  reach  England  make  a  mild  and  soft  cli- 
mate, while  Labrador  is  cold  and  sterile. 

Sea  level  temperatures  are  quite  different  from 
those  of  mountain  tops.  A  mountain  15,000  feet 
high,  even  at  the  equator,  would  have  a  temperature 
about  equal  to  that  of  the  sea  level  at  the  Arctic 
Circle. 

There  is  a  great  difference  in  the  United  States  in 
the  climate  of  the  Pacific  slope  and  that  of  the  inte- 
rior of  the  same  latitude. 

So  that,  although  the  zones  are  bounded  by  mathe- 
matically concentric  circles,  made  practically  by  the 
sun's  path,  the  isothermal  or  heat  lines  curve  accord- 
ing to  the  modifying  conditions  mentioned. 


NOON. 

When  the  sun  is  on  the  meridian  of  a  place  (i.e., 
when  it  has  attained  its  highest  altitude),  it  is  NOON 
at  that  meridian,  and  at  that  meridian  only.  Only 
one  meridian  can  have  noon  at  the  same  instant;  all 
others  are  either  in  A.  M.  or  p.  M.  Bear  in  mind  that 
a  meridian  runs  from  pole  to  pole,  or  half  around  the 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       23 

earth;  consequently  the  antipodal  or  opposite  meridian 
must  be  a  midnight  meridian.  Now,  noon  is  a  point 
exactly  half  way  (sun-dial  time)  between  sunrise  and 
sunset,  and  midnight  a  point  exactly  opposite  noon. 

Of  course,  in  average  or  mean  sun  time  the  fore- 
noon may  be  longer  or  shorter  than  the  afternoon. 

The  earth  turns  uniformly  on  its  axis.  Noon  is 
marching  around  the  world  with  measured  tread. 
One  meridian  after  another  is  brought  opposite  the 
sun. 

The  period  of  the  rotation  is  twenty-four  hours, 
not  a  second  more  or  less. 


LATITUDE  AND  THE  SUN'S  MERIDIAN 
ALTITUDE. 

Latitude  will,  of  course,  affect  the  sun's  meridian 
altitude.  Note  the  height  of  the  sun  in  the  diagram 
on  page  24. 

It  is  arranged  for  March  and  September;  the  sun 
is  vertical  on  the  equator;  the  angle  diminishes  from 
this  (90°)  to  zero  at  either  pole.  At  the  two  tropics 
the  altitude  is  66><0  and  at  the  two  circles  23^°  at 
noon. 

The  angle  for  June,  the  highest  limit  north,  when 
the  sun  is  vertical  on  the  Tropic  of  Cancer,  will 


24       CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

extend  23^°  beyond  the  North  Pole,  so  that  at  the 
North  Pole  the  meridian  altitude  would  be  23^°. 
The  angle  for  December  would  just  touch  the  Arctic 


SI 

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LATITUDE—  SOUTH. 

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September  21. 

Circle;  consequently  the  sun  would  not  appear  above 
the  horizon  from  that  point  to  the  North  Pole. 

March  21  and  September  21  the  angle  would  just 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       25 

touch  either  pole.  The  sun  would,  therefore,  be  on 
the  horizon  at  midday  at  those  points. 

The  sun's  declination- is  its  distance  north  or  south 
of  the  equator. 

To  find  the  sun's  meridian  altitude,  add  its  declina- 
tion for  that  day  to  the .  co-latitude  of  the  place  (the 
co-latitude  of  a  place  is  its  latitude  deducted  from 
90);  that  is,  if  the  latitude  and  declination  are  both 
of  the  same  name;  but  if  one  is  north  and  the  other 
south,  it  must  be  deducted  instead  of  added.  For 
instance,  we  have  stated  that  the  sun's  meridian  alti- 
tude for  the  Arctic  Circle  (66><0  north)  for  the  2ist 
of  June  would  be  47°.  '  The  declination  of  the  sun 
for  this  da}-  is  23^2°  north,  and  the  co-latitude  of 
66^°  would  be  23><°;  this  added  to  the  declination 
equals  47°,  which  is  the  meridian  altitude  of  the  sun 
for  that  date.  When  the  sun  is  at  a  meridian  alti- 
tude of  45°,  his  rays  would  fall  perpendicularly  on 
the  side  of  a  hill  facing  the  south  at  an  angle  of  45°. 


26       CURIOSITIES  OF  LATITUDE  A;ND  LONGITUDE. 

Latitude  does  not  affect  TIME,  except,  as  we  have 
stated,  the  times  of  sunrise  and  sunset.  I  have 
explained  how  the  meridian  altitude  of  the  sun  can 
be  found  from  the  latitude  and  the  sun's  declination. 
Here  is  a  simple  rule  for  finding  latitude: 

LATITUDE— HOW  OBTAINED. 

From  90°  (corrected  89° — 48')  deduct  the  sun's  ob- 
served altitude,  which  will  equal  the  zenith  distance 
(make  Z.  D.  north  if  sun  bears  south,  or  south  if  the 
sun  bears  north).  Add  to  zenith  distance  the  sun's 
declination,  if  both  same  name,  and  the  sum  will  be 
the  latitude.  If  one  is  north  and  the  other  is  south, 
deduct;  the  latitude  will  then  be  the  same  name  as  the 
greater  number.  June  2ist  the  sun's  meridian  alti- 
tude at  the  Arctic  Circle  is  47°;  90  —  47  —  43  (its 
Z.  D.)  added  to  23^°  (Sun's  N.  Dec.)  =  66}^°,  or  the 
latitude. 

On  the  2ist  of  December  the  conditions  we  have 
stated  for  June  in  regard  to  meridian  altitude  north  "and 
south  would  be  reversed.  The  sun  is  vertical  on  the 
earth  only  at  places  between  the  tropics.  The  mer- 
idian altitude  of  the  sun  is  therefore  never  90°  or 
vertical  (in  the  zenith)  at  any  place  outside  of  the 
Torrid  Zone.  (Never  vertical  in  the  United  States. ) 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       27 

The  sun  is  vertical  on  the  equator  only  on  the  2ist  of 
March  and  2ist  of  September;  on  the  Tropic  of 
Cancer  on  the  2ist  of  June  and  on  the  Tropic  of 
Capricorn  on  the  2ist  of  December.  On  March  21 
and  September  21  the  sun's  meridian  altitude  equals 
the  co-latitude  of  a  place;  for  instance,  the  latitude 
of  Chicago  is  42°  N. ;  the  co-latitude  is  90  —  42°= 
48°,  the  meridian  altitude  at  that  date. 

90  minus  the  altitude  of  a  heavenly  body  equals  its 
zenith  distance. 

90  minus  the  latitude  of  a  place,  equals  its  co-lati- 
tude or  complement. 

90  minus  the  sun's  declination  equals  its  polar 
distance.  > 

Latitude  affects  the  apparent  place  of  the  rising 
and  setting  of  the  sun.  In  March  and  September,  or 
at  the  two  equinoxes,  the  sun  rises  due  east  and  sets 
due  west,  but  as  he  advances  northward  or  southward 
his  rising  and  setting  points  advance  northward  or 
southward.  On  the  2ist  of  June  the  sun  rises  23^ 
degrees  north  of  east,  but  for  all  places  north  of  the 
Tropic  of  Cancer  the  sun  will  be  south  of  the  observer 
at  noon.  If  the  sun  is  due  south  at  noon,  he  will  be 
due  north  at  midnight. 

In  summer,  in  the  higher  latitudes,  the  sun  rises 


28       CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

and  sets  farther  and  farther  from  the  east  and  west 
points  until  it  is  due  north. 


MIDNIGHT 


DIAGRAM  SHOWING  THE  POINTS  OF  SUN'S  RISING  AND 
SETTING  JUNE  21. 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       29 

'THE  PHENOMENA  OF  DAY  AND  NIGHT. 

The  phenomena  of  day  and  night  are  phenomena 
belonging  to  both  latitude  and  longitude.  On  the 
2ist  of  June,  two-thirds  of  the  night  shadow  on  the 
earth  is  below  the  equator  and  one-third  of  the  night 
shadow  is  above  it.  On  the  2ist  of  December  these 
conditions  are  reversed.  The  shadow  of  night  on  the 
earth  and  the  illuminated  portions  are  always  exactly 
half  and  half  (the  shadow,  however,  includes  dawn 
and  twilight),  but  the  position  of  the  shadow  is  depen- 
dent upon  the  time  of  year  and  latitude.  The  shadow 
is  always  pivoted  at  the  equator,  consequently  day 
and  night  at  this  place  are  always  equal.  Twice  a 
year,  March  and  September,  the  shadow  is  perpen- 
dicular to  the  equator;  that  is,  the  line  of  the  shadow 
is  co-incident  with  the  meridian  line  to  which  it  may 
be  pivoted.  The  shadow  is  always  at  a  right  angle 
to  the  sun,  so  that  if  the  sun  is  north  the  shadow  is 
south;  and  if  the  sun  is  south  the  shadow  is  north. 
Whatever  angle  the  sun  makes  with  the  equator,  a 
corresponding  angle  of  the  night  shadow  is  made 
with  the  meridian.  On  the  2ist  of  June  and  the  2ist 
of  December  the  line  of  the  shadow  cuts  the  Arctic 
Circle  on  the  one  hand  and  the  Antarctic  Circle  on 
the  other,  and  the  angle  is  23^°.  At  all  other  times 


30       CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

of  the  year  the  shadow  encroaches  upon  the  polar 
regions  until  the  shadow  becomes  perpendicular,  as 
stated,  March  21  and  September  21;  so  that  every 
portion  of  the  earth  has  an  equal  amount  of  shadow 
and  sunshine  at  some  time  of  the  year  from  pole  to 
pole. 

There  is  a  wonderful  compensation  balance  in  the 
earth.  There  is  not  a  spot  on  its  surface  that  does 
not  enjoy,  at  some  time,  its  equal  share  of  the  oppo- 
sites  of  night  and  day,  or  sunshine  and  shadow,  heat 
and  cold,  summer  and  winter,  etc.  This  is  especially 
true  of  sunshine.  All  parts  of  the  earth  have  an 
equal  amount  of  sunshine  in  the  yearly  distribution 
of  sunshine. 

Take,  for  instance,  the  latitude  of  New  York  at 
the  summer  solstice,  June  21;  New  York  has  fifteen 
hours  of  sunshine  and  nine  hours  of  shadow.  The 
opposite  latitude  south,  say  a  place  in  New  Zealand, 
has  nine  hours  of  sunshine  and  fifteen  hours  of  shadow. 
Now,  take  December  21;  the  winter  solstice:  New 
York  has  nine  hours  of  sunshine  and  fifteen  of  shadow, 
while  New  Zealand  has  fifteen  of  sunshine  and  nine 
of  shadow. 

The  law  ol  compensation  is  exemplified  in  the 
distribution  of  heat  and  cold.  The  greatest  heat  is 
of  course  in  the  Torrid  Zone,  where  the  rays  of  the 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.      31 

sun  fall  perpendicularly,  and  the  greatest  cold  is  in  the 
Frigid  Zones,  where  the  rays  of  the  sun  fall  obliquely 
upon  the  earth.  But  here  comes  in  the  wonderful 
compensator}-  balance  of  unequal  day  and  night, 
thus  in  a  measure  equalizing  the  heat. 

Heat  is  cumulative.  If  more  heat  is  received  by 
day  than  can  be  radiated  away  at  night,  it  grows  and 
accumulates. 

Thus,  in  the  Northern  Hemisphere,  though  the 
longest  day  is  reached  in  June,  the  hottest  days  are 
in  July  and  August. 

At  the  equator,  or  in  the  hot-belt,  days  and  nights 
are  about  equal  in  length,  so  that  when  the  sun  sets 
at  b  o'clock  the  earth  begins  to  cool  and  the  heat 
gathered  during  the  day  is  radiated  away  during  the 
twelve  hours  of  the  night. 

Travelers  who  go  to  southern  states  in  summer  re- 
mark upon  the  coolness  of  the  nights,  notwithstand- 
ing the  hot  days. 

Thus,  this  law  of  compensation  (owing  to  the  diur- 
nal rotation  and  the  inclination  of  the  axis  of  rota- 
tion), makes  all  parts  of  our  earth  habitable  and  adapted 
to  the  needs  of  man. 

Day  and  night  must  always  together  equal  24 
hours.  If  the  day  exceeds  12  hours,  the  night  is 
less  than  12  hours  in  exact  proportion.  Day  and  night 


32       CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

are  differential  for  all  latitudes  and  24  hours  is   trie 
total. 

Knowing  the  length  of  either  the  day  or  night  (by 
day  and  night  I  mean  the  time  between  the  rising 
and  setting,  or  the  setting  and  the  rising  sun)  it  is 
easy  to  get  the  hours  of  sunrise  or  sunset;  or,  know- 
ing the  hours  of  sunrise  and  sunset,  it  is  easy  to  get 
the  length  of  the  day  or  night. 

Double  the  hour  of  sunrise  for  the  length  of  the 

night, 
And  double    the  hour  of  sunset  for  the  length  of 

the  day; 
Or  take  half  the  length   of  the   day  for  the  hour 

of  sunset, 

And  half  the  length  of  the  night  for  the  hour  of 
sunrise. 

CO-INCIDENT  PHENOMENA. 

The  same  latitude  phenomena  occurs  in  the  co-iu- 
cident  months  as  follows: 

May  and    July, 

April  and     August, 

February    and     October, 
January      and     November. 

In  shape  the  earth  is  an  oblate  spheroid,  i.  e.,  a 
sphere  slightly  flattened  at  the  poles,  with  an  excess 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       33 

of  matter  at  the  equator.  Its  polar  diameter  is  7,899 
and  its  equatorial  diameter  7,925  statute  miles;  the 
value  of  a  degree  therefore  at  the  poles  is  0.7  of  a 
mile  greater  than  at  the  equator.  Its  circumference 
is  24,897  statute  miles.  Latitude  is  measured  north 
and  south  from  the  equator,  and  the  latitude  of  a 
place  is  its  distance  in  degrees  north  or  south  of  the 
equator.  Probably  sea  levels  in  corresponding  lati- 
tudes north  or  south  of  the  equator  are  equi-distant 
from  the  earth's  center. 


THE  NORTH  POLAR  STAR. 

Latitude  affects  the  height  of  the  Pole  Star,  which  is 
always  at  an  altitude  equal  to  the  observer's  latitude. 
The  farther  we  go  north,  the  higher  the  Pole  Star 
appears  above  our  horizon. 

To  an  observer  at  the  equator,  the  Pole  Star  will  be 
on  his  horizon.  Standing  at  the  North  Pole  this  star 
would  be  in  his  zenith.  At  any  latitude  between 
these  two  places  the  star  will  appear  at  a  correspond- 
ing altitude.  At  New  York,  for  instance,  the  star 
will  appear  about  41  degrees  above  the  horizon. 
At  the  latitude  of  Chicago,  42  degrees. 

At  London  it  would  be  52,  and  at  Christiania,  Nor- 


34       CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

way,  the  star  would  appear  about  60  degrees  above 
the  horizon. 

Every  degree  we  move  north,  the  North  Star  moves 
a  degree  higher  in  the  heavens.  It  is  easy  to  find 
the  value  of  a  degree  of  latitude,  for  if  a  ship  sails 
about  69  miles  north  or  south  the  Pole  Star  would 
move  a  degree  north  or  south ;  hence  69  miles  must  be 
about  the  value  of  a  degree  of  latitude.  Note  the 
table  on  pp.  72-73.  This  will  show  the  exact  value 
of  a  degree  of  latitude;  it  varies  from  68.698  to 
69.392,  i.  e.,  expressed  in  English  statute  miles. 

The  diurnal  (daily)  rotation  (apparent)  of  the  north- 
ern heavens  is  contrary  to  the  hands  of  a  watch. 

The  earth  is  our  observatory,  but  bear  in  mind  it  is 
a  movable  observatory.  The  apparent  movements  of 
the  celestial  bodies  are  due  solely  to  the  movements 
of  our  earth.  The  center  of  gravity  possibly  may  not 
lie  in  the  center  of  our  earth.  The  greater  land  por- 
tion of  the  earth  is  in  the  Northern  Hemisphere,  and 
the  greater  part  of  this  land  portion  is  in  the  eastern 
half,  between  15  W.  and  160  E.  Long. 

The  magnetic  pole  is  not  the  North  pole,  but  is  in 
about  105°  West  Long,  and  75°  North  Lat.;  the  com- 
pass will  not  therefore  always  point  North.  The 
variation  must  be  known  and  corrected  by  the  navi- 
gator. 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.      35 

As  regards  the  moving  circle  of  rotation,  East  and 
West  are  arbitrary  terms.  There  is  no  East  or  West 
in  a  circle. 


DIRECTION    OF   DIURNAL    ROTATION. 

The  diurnal  rotation  of  the  earth   causes  an  appar- 
ent diurnal  rotation  of  the  heavens.      In  the  northern 


36      CURIOSITIES  OF  LATITUDE   AND  LONGITUDE. 

hemisphere  it  will  be  seen  that  the  north  celestial 
pole  is  the  point  about  which  the  heavens  revolve. 
Here  a  star  has  no  diurnal  motion.  The  north  celes- 
tial pole  is  in  a  line  with  the  axis  of  the  earth.  A 
prolonged  exposure  photograph  of  the  circumpolar 
stars  (i.  e.,  those  stars  which  are  above  the  observer's 
horizon)  show  concentric  rings  of  light.  Even  the 
Pole  Star  itself  leaves  a  little  trail  of  light  as  it  revolves 
around  the  true  pole,  about  a  degree  and  a  half  from 
it.  The  true  celestial  pole  is  that  point  in  the  heav- 
ens where  the  axis  of  the  earth,  if  prolonged,  would 
pierce  the  heavens. 

Although  the  diurnal  rotation  of  the  earth  is  unvary- 
ing, this  great  clock  having  kept  time  through  all 
the  ages  without  the  loss  of  a  second,  yet  the  axis 
of  the  earth  is  not  (according  to  recent  investiga- 
tions and  experiments)  a  rigid  or  fixed  line  in 
the  earth;  i.  e.,  the  North  Pole  does  not  maintain  an 
absolutely  fixed  position.  This,  of  course,  affects  lat- 
itudes. 


CURIOSITIES  OF  LATITUDE  AND   LONGITUDE.       37 

DAWN    AND    TWILIGHT. 

Latitude  affects  the  amount  and  duration  of  twi- 
light; the  duration  varies  with  the  season  and  the 
latitude,  the  longer  twilights  existing  in  the  north- 


TWILIGHT    PROJECTION. 


38      CURIOSITIES  OF  LATITUDE   AND   LONGITUDE. 

ern  latitudes  (in  summer),  and  in  the  southern  latitudes 
(in  winter).* 

The  reason  for  this  is  that  the  greater  the  distance 
from  the  equator  north  and  south,  the  more  oblique  is 
the  line  of  the  setting  or  rising  sun  with  the  horizon; 
consequently  the  greater  length  of  time  occupied  in 
reaching  the  18°  limit  of  reflection.  The  sun  ap- 
proaching the  horizon  vertically,  reflection  would  dis- 
appear much  sooner  than  if  he  approached  it  at  an 
oblique  angle. 

Dawn  and  twilight  are  of  equal  duration.  They 
are  both  included  between  the  setting  and  rising  of 
the  sun.  Twilight  continues  until  the  sun  is  18°  be- 
low the  horizon.  Dawn  begins  when  the  sun  is  18° 
from  rising. 


CHANGES  IN   THE   APPEARANCE   OF   THE 
HEAVENS. 

Another  curiosity  of  latitude  is  the  change  in  the 
appearance  of  the  heavens  at  different  points. 

*It  should  be  borne  in  mind  that  in  speaking  of  summer  and 
winter,  we  mean  that  portion  of  the  year  representing  the  summer 
and  winter  of  the  Northern  Hemisphere.  December  is  the  sum- 
mer of  the  Southern  Hemisphere  and  June  the  winter  season. 


CURIOSITIES  OF  LATITUDE  AND   LONGITUDE.       39 

On  the  equator  at  latitude  zero,  stars  will  rise  and 
set  vertically,  cutting  the  horizon  at  right  angles.  At 
the  poles  or  latitude  90°,  the  stars  would  neither 
rise  nor  set,  but  would  revolve  around  the  pole 
in  concentric  circles  at  altitudes  corresponding  to  their 
declinations.  The  moon  would  be  visible  for  about 
two  weeks,  and  the  sun  for  six  months  at  a  time. 

At  any  latitude  between  the  equator  and  the  poles, 
the  stars  would  rise  and  set  obliquely. 

LATITUDE  AFFECTS  GRAVITY. 

A  body  would  weigh  more  at  the  poles  than  at  the 
equator,  but  if  weighed  with  ordinary  weight  balances 
the  difference  would  not  show,  as  the  weights  them- 
selves would  be  affected  as  well  as  that  which  is 
weighed. 

A  pendulum  swings  faster  at  the  poles  than  at  the 
equator.  A  pendulum  clock  that  would  keep  accu- 
rate time  at  the  equator,  would  gain  3  yz  minutes  a 
day  at  the  poles;  moreover,  as  a  pendulum  would 
swing  in  a  true  plane,  the  rotation  of  the  earth  would 
cause  it  to  form  a  star  marked  upon  the  surface  of  the 
globe  could  it  swing  about  the  pole. 

Such  are  some  of  the  curiosities  of  latitude.  We 
might  recapitulate  some  of  the  effects,  as  follows: 


40      CURIOSITIES  OF  LATITUDE  AND   LONGITUDE. 

1.  Varying  lengths  of  day  and  night. 

2.  The  hours  of  sunrise  and  sunset. 

3.  The  angle  of  the  sun. 

4.  The  place  of  the  sun's  rising  and  setting. 

5.  The  peculiar  angles  of  the  rising  and  setting 

of  stars. 

6.  The  position  of  the  night  shadow. 

7.  Variation  in  length  of  degrees. 

8.  Height  of  the  Pole  Star. 

9.  The  circles  of  perpetual  apparition  and  occul- 

tation. 

10.  Twilight  and  dawn. 

11.  Gravity.  • 

12.  The  pendulum. 

The  curiosities  of  latitude  mentioned  are  those 
which  are  due  solely  to  the  motions  of  the  earth.  I 
have  not  touched  on  the  physical  aspects  of  latitude 
except  incidentally. 

The  work  is  intended  to  show  those  phenomena 
which  come  within  the  reach  and  scope  of  Mathemat- 
ical Geography. 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.         41 


LONGITUDE  AND  TIME. 

LONGITUDE 

is  the  angular  distance  between  any  two  meridians. 
It  is  reckoned,  east  or  west,  from  any  given  meridian, 
called  a  first  or  prime  meridian.  Meridian  circles 
run  around  the  earth  north  and  south,  and  a  meridian 
reaches  from  pole  to  pole.  Meridian  lines  all  con- 
verge at  the  poles,  and  cut  the  equator  at  right 
angles.  The  greatest  longitude  any  place  can  have 
is  1 80°,  or  half  around  the  globe.  Longitude  is  ex- 
pressed in  degrees,  minutes  and  seconds. 

WHAT  IS  TIME  ? 

A  part  of  duration. 

The  system  of  those  relations  which  any  event  has 
to  any  other,  past,  present  or  future;  an  arc  cut  out 
of  the  circle  of  eternity. 

Time  is  personified  as  an  old  man,  bald-headed, 
but  having  a  forelock,  and  carrying  a  scythe  and 
hour-glass. 


42      CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

Tempus  (L.),  Temps  (P.),  Tempo  (P.  I.),  whence 
temporal,  temporary,  etc. —  Cent.  Die. 

Chronos — Time.     Chronology — Reckoning  of  time. 

Time  has  been  compared  to  a  stream,  or  the  flow  of 
a  river;  the  part  that  goes  by  now  will  never  pass 
again. 

Time  is  a  procession  of  seconds,  minutes,  hours 
and  days,  months,  years  and  centuries,  ever  march- 
ing on. 

How  is  time  measured  ?  What  is  our  chronometric 
register?  What  is  the  standard  unit? 

THE  EARTH  OUR  CLOCK. 

The  axial  rotation  of  the  earth  once  in  24  hours, 
or  one  day,  gives  us  our  exact  standard  of  measure- 
ment. 

By  the  word  day,  we  mean  the  whole  24    hours,  or 
the  period  of  one  rotation  of  the  earth  upon  its  axis. 
From  dial,  dies,  come  diary,  diurnal,  day. — Cent. 
Die. 

Day  and  night  must  always  equal  24. 
60  seconds— i  minute. 
60  miriutes=i  hour. 
24  hours     =i   day,  or  period  of  the  Earth's 

rotation. 
24  hours=i44o  minutes,  or  86,400  seconds. 


CURIOSITIES  OF  LATITUDE   AND   LONGITUDE.      4.3 

The  earth,  in  its  rotation,  obeys  an  original  im- 
pulse. This  movement  of  the  earth  does  not  come 
under  the  law  of  universal  gravitation.  When  a  body 
turns  upon  a  true  and  symmetrical  axis  and  gravity 
is  not  brought  into  play,  the  axis  will  maintain  its 
unvarying  position. 

A  gyroscope  top  illustrates  this.  When  set  in 
motion,  the  axis  always  maintains  the  direction  in 
which  it  is  placed.  There  may  be  two  movements 
of  the  gyroscope  top — the  one  a  rapid  rotation  on  its 
axis,  the  other  a  slow,  conical  movement  of  its  axis, 
owing  to  a  rotation  of  the  top,  frame  and  all. 

The  earth  was  set  spinning  with  the  northern  end 
of  its  axis  pointing  to  the  north  celestial  pole,  and 
that  position  it  still  maintains. 

It  is  true  there  is  a  slow  circular  motion  of  the  pole 
of  the  earth  around  the  pole  of  the  ecliptic,  causing 
the  precession  of  the  equinoxes,  i.e.,  the  zenith  of  the 
poles  change  about  20"  annually.  In  time,  therefore, 
Polaris  will  cease  to  be  the  Pole  Star.  There  is  also 
a  slight  oscillation  of  the  pole  itself,  but  practically 
the  axis  maintains  its  true  position. 

Polaris,  the  bright  polar  star,  is  the  jewel  in  which 
the  axis  is  pivoted,  though  at  present  Polaris,  strictly 
speaking,  is  i°  16'  from  the  true  north  celestial  pole. 
The  earth  turns  upon  its  axis,  or  polar  diameter,  in 


44      CURIOSITIES  OF  LATITUDE  AND   LONGITUDE. 

an  inclined  position  of  23^°,  in  exactly  23  hours,  56 
minutes,  4^  seconds,  expressed  in  mean  solar  time, 
from  west  to  east,  as  do  all  the  planets. 


A  SIDEREAL  DAY. 

This  is  a  sidereal  day.  It  is  the  length  of  time 
that  elapses  between  two  successive  transits  of  the 
same  fixed  star  across  a  meridian. 

Let  not  the  student  be  confused  because  a  sidereal 
day  is  shorter  than  a  mean  solar  day. 

There  are  exactly  24  sidereal  hours  in  a  sidereal  day, 
and  exactly  24  mean  solar  hours  in  a  mean  solar  day, 
but  a  sidereal  day  expressed  in  mean  solar  time  is  4 
minutes  shorter  than  a  mean  solar  day.  As  regards 
the  earth,  the  sun  moves,  while  the  stars  do  not. 

The  gain  of  mean  solar  over  a  sidereal  day  of  4  min- 
utes a  day,  amounts  to  2  hours  a  month,  or  i  day  a 
year.  A  sidereal  clock  (such  as  are  used  in  observa- 
tories) and  a  mean  solar  clock,  therefore,  do  not 
coincide,  except  on  the  2ist  of  March.  The  hands 
would  then  agree.  The  difference  of  24  hours  would 
not  appear.  Like  the  hands  of  a  watch,  they  are  not 
together  at  any  hour  except  12  o'clock. 

The  earth,  in  its  diurnal  rotation  sweeps  the  entire 
circle  of  the  heavens.  All  circles  contain  exactly 


CURIOSITIES  OF  LATITUDE  AND    LONGITUDE.      45 

360°.  The  360°  of  this  circle  are  traversed  in  exactly 
24  hours,  and  as  360-^24=15,  it  is  evident  that  each 
hour  of  the  24,  the  earth  passes  through  just  15°. 

Now  the  day  contains  24  hours,  1440  minutes  or 
86,400  seconds,  and  the  360°  contains  21,600  minutes 
or  i,  296,000  seconds ;  hence  the  earth  will  pass  through 
15°  in  one  hour,  15'  in  one  minute,  and  15"  of  arc  in 
one  second. 

The  accuracy  and  steadiness  of  the  turning  of  the 
earth  are  so  remarkable  that  each  fractional  part  of 
the  24  hours  will  show  an  exact  proportionate  num- 
ber of  degrees,  minutes  and  seconds  of  arc  passed 
over;  in  fact,  when  the  last  second  of  the  24  hours  is 
passed,  the  last  second  of  the  1,296,000  seconds  of 
arc  is  also  finished. 

A  WONDERFUL  CLOCK. 

The  next  beat  of  the  clock  begins  the  first  15"  of 
the  circle  again,  and  every  beat  of  the  pendulum 
thereafter  carries  the  earth  through  15"  of  arc. 

When  we  consider  the  accuracy  of  this  magnificent 
clock,  we  are  astonished.  The  best  time-keepers  are 
lever  escapements  and  chronometer  balances;  watches 
of  high-class  makes,  with  care  in  wearing,  will  run 
within  one  second  per  week.  Tiffany  of  New  York 


46      CURIOSITIES  OF  LATITUDE  AND   LONGITUDE. 

has  records  of  watches  running  ten  months  with  a 
variation  of  only  seven  seconds. 

Full  chronometers  are  not  in  use  for  pocket  wear; 
they  are  liable  to  be  affected  by  any  sudden  motion 
of  the  wearer. 

Our  chronometer  is  liable  to  no  accidents;  it  needs 
no  oiling  or  cleaning;  it  never  runs  down.  No  clock 
that  was  ever  constructed  can  ' '  keep  time' '  with  the 
earth.  This  clock  is  adjusted  to  heat,  cold  and  posi- 
tion. It  is  self-winding,  never  gets  out  of  order,  and 
is  synchronized  -to  beat  with  the  stars.  It  has  not  lost 
a  beat  through  all  the  ages;  that  is,  the  time  of  its 
rotation  has  not  varied  in  thousands  of  years. 

The  star  that  is  cut  in  two  by  the  line  in  the  field 
of  the  transit  telescope  at  8  o'clock,  sidereal  time, 
tonight,  will  be  cut  in  two  by  the  same  line  at  pre- 
cisely 8  o'clock,  sidereal  time,  tomorrow  night,  and 
the  next  night,  and  so  on  through  the  years  and  ages. 

The  figures  on  p.  47  represent  two  sections  cut  from 
a  globe  and  a  Mercator  map,  respectively.  The 
space  represents  one  hour  or  15°.  It  will  be  seen 
that  all  the  parallel  horizontal  lines  and  spaces  have 
the  same  value,  both  in  time  and  degrees. 

Time  and  longitude  are  synonymous. 

It  will  be  observed  that  a  point  at  u^4"  moves  very 
slowly  compared  with  a  point  at  "/),"  yet  the  time 


CURIOSITIES  OF  LATITUDE   AND   LONGITUDE.       47 


occupied  will  be  precisely  the  same.     "Z>"  represents 
the  equator. 

POLE 


EQUATOR 


A  point  on  the  earth's  surface  at  the  equator  moves 
toward  the  east  at  the  rate  of  about  1,000  miles  an 
hour,  because  the  earth's  equatorial  circumference  is 
about  25,000  miles,  and  as  it  takes  24  hours  for  one 
complete  rotation,  a  point  here  would  move,  in  one 
hour,  one  twenty-fourth  of  the  circumference,  or 
about  1,000  miles.  This  motion  is  reduced  to  noth- 
ing at  the  poles. 


48      CURIOSITIES  OF  LATITUDE  AND   LONGITUDE. 

At  the  latitude  of  New  York,  the  motion  is  about 
800  miles  per  hour,  and  at  the  latitude  of  Christiania, 
it  is  reduced  to  500  miles  per  hour;  but  a  point  on 
the  equator  passes  over  15°  in  one  hour;  so  does  a 
point  at  the  6oth  parallel. 

The  hare  at  the  equator  will  arrive  at  his  destina- 
tion at  the  same  instant  as  the  tortoise  at  the  6oth 
parallel.  All  hour  circles  have  the  same  value, 
whether  they  contain  60  miles  or  one  mile  to  a 
degree. 

Longitude  is  not  synonymous  with  miles.  It  is 
not  measured  in  miles,  but  in  degrees.  An  hour 
angle  contains  15°,  whether  it  contains  900  miles  (as 
at  the  equator),  or  one  mile  (as  at  the  8gih  parallel). 

See  table  on  page  70. 


CURIOSITIES  OF  LATITUDE  AND    LONGITUDE.       49 


THE  SUCCESSION   OF  DAYS. 

Now  let  us  see  how  the  days  follow  each  other. 
When  and  where  does  a  day  begin?  Where  does 
Saturday  or  Sunday  begin?  Is  Sunday  universal 
over  the  earth,  or  is  it  partly  Sunday  and  partly 
Saturday  or  Monday  or  some  other  day?  Is  today 
the  same  day  of  the  month  at  New  York  and  New 
Zealand,  at  Bombay  and  at  San  Francisco? 

Let  me  say  that  there  is  always  day  and  night  on 
the  globe — that  is  to  say,  somewhere  it  is  always  per- 
petual day  and  somewhere  perpetual  night  around 
the  world.  The  sun  is  always  waking  up  the  morn- 
ing and  chasing  away  the  shadows  of  night. 

"Somewhere  the  glorious  morning  hues, 

The  eastern  sky's  adorning; 
Somewhere  upon  this  earth  of  ours 

You'll  find  'tis  always  morning." 

And  night  is  always  following  up  the  day.  Where, 
then,  does  the  day  begin?  Now  suppose  we  begin 
our  investigation  of  this  subject  at  Chicago,  near  the 


50      CURIOSITIES  OF  LATITUDE   AND  LONGITUDE. 

9oth  meridian  of  west  longitude,  on,  say  Saturday 
morning  at  6  o'clock,  we  shall  find  the  local  time  of 
New  York  to  be  7  o'clock  A.  M.;  10  A.  M.  at  the 
Azores  in  mid- Atlantic,  noon  at  London,  7.30  P.  M. 
at  Pekin,  China,  while  at  New  Zealand  the  day  is 
drawing  to  a  close.  Thus  it  is  early  morning  at 
Chicago,  breakfast  time  in  New  York,  dinner  time  in 
London,  and  supper  time  in  Pekin  all  in  the  same 
day. 

Suppose  now  we  take  a  step  to  the  westward  of 
Chicago.  It  is  4  A.  M.  at  San  Francisco,  and  1.30 
A.  M.  at  Honolulu.  But  all  this  is  Saturday,  a  civil 
day  twenty-four  hours  long,  and  as  the  civil  day 
begins  at  midnight,  it  is  evident  that  this  particular 
day  was  born  a  little  to  the  west  of  Honolulu.  Civil 
days  are  divided  into  periods  of  twelve  hours  each; 
hence  all  clock  dials  are  divided  into  twelve  spaces  of 
one  hour  each. 

To  a  person  living  at  Honolulu,  then,  Saturday 
has  just  begun;  to  one  living  in  London  it  is  noon  of 
Saturday;  to  one  living  in  New  Zealand  Saturday  is 
nearly  over  and  he  is  sleeping  into  Sunday  morning; 
to  a  resident  of  Chicago,  Sunday  is  eighteen  hours 
away,  while  to  a  Londoner,  it  is  but  twelve  hours 
away.  Now  it  is  clear  that  by  the  time  Sunday  gets 
to  Honolulu,  it  is  Monday  morning  at  "New  Zealand. 


CURIOSITIES  OF  LATITUDE  AND   LONGITUDE.       51 

Though  Honolulu  and  New  Zealand  are  not  far  apart 
in  longitude,  they  are  widely  apart  as  regards  lati- 
tude, the  one  being  in  north  and  the  other  in  south 
latitude.  But  latitude  does  not  affect  time. 

People  who  live  on  the  opposite  side  of  the  earth, 
or  Antipodes,  have  opposite  latitudes,  longitudes, 
days,  nights  and  seasons. 

The  people  of  Europe  have  observed  their  Sunday 
while  the  people  of  the  United  States  are  sleeping, 
and  while  the  people  of  the  United  States  are  observ- 
ing their  Sunday,  the  people  of  Europe  are  sleeping 
into  Monday  morning.  It  is  evident,  therefore,  that 
for  purposes  of  commerce  and  navigation,  there  must 
be  a  beginning  somewhere  of  a  day,  at  some  point  on 
the  earth  a  day  must  begin  and  end,  that  is,  the  com- 
mercial civil  day;  Saturday,  for  instance,  the  day  we 
have  just  been  describing. 

WHERE  DOES  THE  DAY  BEGIN? 

The  point  opposite  noon  would  evidently  be  the 
best  TIME  point,  and  a  point  farthest  removed  from 
land  and  civilization,  the  best  GEOGRAPHICAL  point 
with  which  to  begin  a  new  day.  I/mdon  being  the 
metropolitan  city  of  the  earth,  the  geographical  center 
of  the  land  portion  and  the  commercial  center,  it  is 


52      CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

fitting  also  that  it  be  the  time  center,  and  that  the 
meridian  of  London  should  be  the  first  meridian.  A 
point  opposite  London  in  the  Pacific  ocean  is  a  point 
farthest  removed  from  this  center  of  the  world's 
civilization;  it  is  therefore  the  best  point  to  begin  the 
day. 

The  maritime  powers  of  the  world  have  agreed 
to  regard  this  iSoth  degree  of  longitude  from 
London  (or  Greenwich)  as  the  point  where  the  day 
changes.  This  meridian  therefore  leads  the  day. 
Its  passage  under  the  iSoth  or  midnight  celestial 
meridian  marks  the  beginning  of  a  new  day  for  the 
earth ;  here  today  becomes  tomorrow.  We  have  a  new 
date  for  the  month,  and  a  new  day  for.  the  week  in 
the  transition.  It  is  here  that  Saturday  ends  and 
Sunday  begins. 

It  is  here,  then,  that  Sunday  was  born,  just  to  the 
west  of  Honolulu,  but  bear  in  mind  that  the  day 
travels  westward,  therefore  this  new  born  day  does 
not  visit  Honolulu  until  it  has  made  the  circuit  of 
the  round  globe.  Sunday  travels  west  via  New 
Zealand. 

Honolulu  and  New  Zealand  are  only  about  30° 
apart  in  longitude,  but  they  are  a  whole  day  apart  as 
regards  any  particular  day,  because  the  point  at  which 
the  day  changes  lies  between  them.  Again,  it  is 


CURIOSITIES  OF  LATITUDE  AND    LONGITUDE.       53 

evident  that  Sunday  is  a  long  way  off  from  Honolulu, 
because  that  place  has  only  just  passed  out  of  Friday 
into  Saturday,  whereas  New  Zealand  is  passing  out 
of  Saturday  into  Sunday. 

Sunday  travels  west,  because  the  earth  travels  east. 
Sunday  must  visit  China,  Russia,  India  and  all  of 
Europe,  must  cross  the  Atlantic  and  the  United 
States  before  it  can  reach  the  Pacific  and  Honolulu, 
and  no  sooner  does  Honolulu  get  out  of  Saturday  into 
Sunday,  than  Monday  morning  appears  at  New  Zea- 
land. 

THE  INTERNATIONAL  DATE  LINE. 

The  international  date  line,  though  practically  the 
iSoth  meridian,  is  a  line  drawn  irregularly  through 
the  Pacific  ocean,  south  through  Behring-  sea;  south- 
west past  the  Aleutian  islands;  south  from  Attu  island 
on  meridian  172°  south,  to  parallel  15°  north;  east  on 
1 5th  parallel  to  i5Oth  meridian  west;  south  on  i5Oth 
meridian  to  parallel  15°  south;  west,  clearing  Society 
islands,  to  meridian  155°  west;  south  to  Tropic  of 
Capricorn;  southwest  by  south  indefinitely. 

The  day  begins  here,  at  the  iSoth  meridian  and 
travels  west,  because  the  earth  travels  east.  When  it 
arrives  at  London  it  is  about  12  hours  old,  at  New 


54      CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

York  about  17  hours  old,  and  at  San  Francisco  about 
20  hours  old. 

When  the  day  arrives  here  at  the  iSoth  meridian, 
it  is  24  hours  old;  it  gradually  grows  less  and  less, 
with  the  new  day  following,  the  old  day  diminishes  and 
the  new  day  increases.  When  noon  arrives  here,  the 
end  of  the  day  is  at  London,  with  the  new  day 
following  close. 

The  preceding  day  is  west  of  the  line,  the  succeed- 
ing day  is  east  of  it. 


The  longitudinal    quadrants    of  the  earth  are   as 
follows : 

XII — NOON — The  initial  meridian — London. 
VI— A.M.— The  goth  meridian  of  W.  L.—  Chicaj 


CURIOSITIES  OF  LATITUDE  AND    LONGITUDE.       55 
MIDNIGHT — The      iSoth     meridian — Pacific 


Oceaff. 

VI— P.M.— Tr^oth  meridian  of  E.  L.— Calcutta. 

These  are  the  four  cardinal  points  of  the  circle. 

In  studying  the  above  diagram,  it  is  necessary  to 
bear  in  mind  the  point  of  view,  which  is  the  iSoth 
meridian,  looking  through  the  globe  to  London.  It 
does  not  represent  the  plane  of  any  parallel,  but  is 
designed  to  show  longitude.  When  XII  (noon)  is  at 
London,  one  day  and  date  prevail  over  the  entire 
earth.  If' noon  is  either  east  or  west  of  London,  parts 
of  two  days  are  in  operation.  When  noon  is  at  London, 
there  is  only  "a  today"  upon  the  earth.  When  noon 
leaves  London,  there  is  "a  today,"  "a  yesterday" 
and  "a  tomorrow"  in  operation. 

Suppose,  for  instance,  noon  had  arrived  at  Chicago- 
Chicago's  antipodal  meridian  is  the  meridian  which 
passes  through  Calcutta.  Therefore,  if  it  is  noon  at 
Chicago  it  is  midnight  at  Calcutta.  All  of  that  portion 
of  the  earth  east  of  Calcutta  is  therefore  in  tomorrow, 
and  there  people  could  say  of  that  portion  of  the  earth 
west  of  Calcutta  (which  would  include  of  course  Chi- 
cago) "that  is  in  yesterday,"- and  everyone  has  "a 
today. ' '  When  it  is  noon  at  London  only  one  day  occu- 
pies the  earth  simply  because  there  are  1 2  hours  either 
side  of  noon,  and  12  hours  in  either  direction  would 


56      CURIOSITIES  OF  LATITUDE  AND   LONGITUDE. 

produce  midnight.  The  opposite  meridian  from  Lon- 
don being  the  iSoth  degree,  of  course,  there  it  would 
be  midnight.  The  antipodal  meridian  of  any  place 
is  the  one  removed  from  it  by  12  hours,  or  180  degrees. 

To  find  your  antipodal  meridian,  deduct  from  180 
your  meridian.  This  will  give  your  opposite  meridian 
in  opposite  longitude.  For  instance,  what  is  the 
opposite  (or  antipodal)  meridian  to  New  York  (75th 
W.  L.)  180 — 75=105;  105  E.  L.  is  the  antipodal  meri- 
dian to  New  York. 

When  noon  leaves  London  on  its  travels  west  (every- 
thing goes  west)  and  arrives  at  the  i5th  degree  of 
west  longitude,  or,  in  other  words,  has  advanced  one 
hour  to  the  west,  the  new  day  starting  at  the  iSoth 
meridian  is  one  hour  old  and  has  advanced  to  the 
i65th  degree  of  east  longitude. 

•We  have  explained  how  the  two  places,  Honolulu 
and  New  Zealand,  are  near  together  and  yet  practic- 
ally a  whole  day  apart,  Honolulu  being,  just  east  of 
the  line  and  New  Zealand  just  to  the  west  of  it  We 
have  explained  that  the  day  travels  west,  so  New 
Zealand  is  the  first  to  see  the  new-born  day.  It  is 
clear,  then,  if  it  is  Friday  (near  midnight)  at  Hono- 
lulu to  the  east  of  the  line  and  Sunday  (near  i  A.  M.) 
to  the  west  of  it,  that  a  ship  which  sails  from  Honolulu 
to  New  Zealand,  or  from  east  to  west,  must  sail  out  of 


CURIOSITIES  OF  LATITUDE  AND   LOXGITUDE.       57 

Friday  into  Sunday,  and  thereby  skips  the  interven- 
ing day  of  Saturday,  and  gains  a  day,  while  vice  versa, 
a  ship  which  sails  from  New  Zealand  (where  Sunday 
has  begun)  to  Honolulu,  where  Friday  has  just  ended 
and  Saturday  begun,  or  from  west  to  east,  must  lose 
a  day,  because  it  has  to  go  back  into  Friday.  Now 
this  change  of  date  at  the  i8oth  meridian  must  npt  be 
confounded  with  the  gain  or  loss  of  time  in  trawling 
east  or  west  with  or  against  the  rotation  of  the  Barth. 
To  gain  or  lose  on  the  sun  we  must  move  our  noon 
point.  The  moment  we  leave  our  position,  i.  e. ,  our 
meridian,  we  gain  or  lose,  just  in  proportion  to  the 
number  of  degrees  passed  over. 

GAIN  OR  LOSS  OF  TIME. 

For  instance,  if  we  leave  New  York  at  the  75th 
meridian  and  sail  east  to  London,  we  have  gained  as 
many  hours  as  fifteen  is  contained  in  seventy-five,  or 
five  hours,  i.  e.,  our  noon  in  New  York  is  five  hours 
back  of  the  noon  we  are  now  experiencing;  or,  in 
other  words,  noon  of  London  is  7  A.  M.  at  New  York, 
and  noon  of  New  York  is  5  p.  M.  of  London.  Here 
we  gain  absolute  time,  and  this  time  is  in  exact  pro- 
portion to  the  number  of  degrees  passed  over.  In  the 
other  case  an  arbitrary  line  changed  our  date  and  put 


58      CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

us  backward  or  forward  in  our  dates.  Moreover  the 
crossing  of  this  iSoth  meridian  makes  us  gain  the 
day  as  we  go  west  and  lose  as  we  go  east.  In  sailing, 
as  regards  the  sun,  just  the  reverse  of  this  is  true. 
We  gain  time  in  sailing  east  and  lose  time  in  sailing 
west,  and  in  the  latter  case  the  time  bears  an  exact 
proportion  to  the  number  of  degrees  passed  over, 
while  in  the  former  we  jump  a  whole  day. 

Every  15°  passed  over  east  or  west  is  one  hour  of 
time,  and  as  there  are  360°  in  the  entire  circuit  we 
should  gain  or  lose  in  making  the  entire  circuit  just 
twenty-four  hours,  or  one  day,  because  360° -f-  15°=  24. 

Now  we  may  creep  over  the  15°  or  fly  over  them — 
the  result  is  just  the  same.  With  Jules  Verne  we  may 
circumnavigate  the  globe  in  eighty  days,  or  we  may 
take  eighty  years  to  do  it.  We  shall  in  either  case 
lose  or  gain  but  twenty-four  hours. 

How  shall  we  reconcile  this  gain  in  traveling  east- 
ward with  the  loss  in  covering  the  i  Both  meridian? 

Now  in  sailing,  say  from  30°  west  of  New  Zealand 
to  30°  east  of  Honolulu  (for  purpose  of  illustration  let 
us  imagine  these  two  places  to  be  on  the  iSoth  meri- 
dian), we  have  passed  to  the  east  60°,  a  four  hours' 
&ain  in  time,  but  in  doing  this  we  crossed  the  line 
going  east,  so  we  lost  a  day.  What  have  we  lost 
or  gained?  Well,  we  have  lost  a  day  and  gained 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       59 

four  hours.  In  other  words  we  have  lost  twenty 
hours. 

Suppose  it  was  10  A.  M.  of  Sunday  30°  west  of  the 
line,  30°  east  of  it  is  2  P.  M.  of  Saturday.  If  Sunday 
was  July  31,  then  we  shall  find  our  date  to  be  Satur- 
day, July  30,  at  2  P.  M.,  because  we  count  back 
twenty  hours  from  10  A.  M.  Sunday. 

So  a  ship  which  sails  east  from  London  around  the 
world  crossing  this  meridian,  will  lose  a  day  and  gain 
half  a  day.  That  is  to  say  if  it  is  noon  Saturday,  July 
31,  at  London,  it  is  midnight  of  Saturday,  July  31, 
at  this  meridian. 

Now  at  this  arbitrary  line  or  the  iSoth  meridian, 
we  have  practically  parts  of  two  days  in  operation, 
while  at  all  other  places  on  the  Earth  there  is  but  one 
day.  On  the  line  we  have  the  midnight  hours  of 
Friday  and  the  early  hours  of  Sunday,  the  rest  of  the 
globe  being  occupied  by  Saturday.  Saturday  is 
flanked  on  the  one  side  by  Friday  and  on  the  other 
by  Sunday/ 

I  have  stated  that  Honolulu  and  New  Zealand  were 
a  whole  day  apart — practically  they  are — yet  this  is 
not  strictly  correct.  The  difference  is  not  exactly  a 
whole  day,  by  putting  it  thus  the  student  at  once 
grasps  the  idea  that  one  place  is  in  one  day  of  the 
week  and  the  other  in  another  day  of  the  week. 


60      CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

The  aim  is  to  make  it  perfectly  clear  why  it  is 
Saturday  in  one  place  and  Sunday  in  another  on  the 
earth. 

CIRCUMNAVIGATING  THE  GLOBE. 

If  a  ship  were  to  circumnavigate  the  globe  on  the 
equator,  at  the  rate  of  900  geographical  miles  a  day, 
it  would  take  just  twenty-four  days  to  do  it,  because 
15°  multiplied  by  sixty,  the  number  of  miles  in  a 
degree  at  the  equator,  would  produce  900,  and  as  15° 
is  one  twenty-fourth  of  the  circumference  it  would 
take  just  twenty-four  days  to  sail  the  360°.  Now  as 
the  meridians  converge  at  the  poles,  the  number  of 
miles  to  a  degree  grows  less  and  less  as  we  approach 
the  poles.  At  60°  north  latitude,  for  instance,  there 
are  only  thirty  miles  to  a  degree,  consequently  a  ship 
sailing  900  miles  a  day  will  take  but  twelve  days  to 
circumnavigate  the  globe  on  this  parallel. 

Time  and  longitude  are  synonymous,  but  not  time 
and  distance. 

We  cannot  measure  miles  east  or  west  without 
knowing  on  what  parallel  they  are  to  be  measured. 
There  is  no  time  and  longitude  at  the  absolute  poles. 
Nor  is  it  needed.  We  cannot  sail  much  nearer  than 
10°  of  the  poles.  The  moment,  however,  we  leave 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       6 1 

the    pole,   the    meridian    lines   have   an    appreciable 
angle,  therefore,  longitude  can  be  computed. 

Now  the  earth  performs  a  complete  rotation  on  its 
axis  in  exactly  twenty-four  hours,  and  in  doing  this 
goes  through  exactly  360°,  and  each  fractional  part  of 
the  twenty-four  hours  will  show  an  exact  correspond- 
ing number  of  degrees  (of  arc)  passed  over.  It  is 
evident  from  this  that  degrees  of  longitude  and 
hours  of  time  are  convertible  and  interchangeable 
terms.  Longitude  means  length  as  latitude  means 
breadth,  though  latitude  has  nothing  to  do  with 
time. 

There  are  21,600  minutes,  or  1,296,000  seconds  of 
arc  in  360°.  Also  there  are  1440  minutes,  or  86,400 
seconds  of  time  in  twenty-four  hours.  Now  by  divid- 
ing degrees  by  hours,  or  minutes  by  minutes,  or 
seconds  by  seconds,  we  shall  see  that  fifteen  degrees  of 
longitude  will  equal  one  hour  of  time,  fifteen  minutes 
of  longitude  one  minute  of  time,  and  fifteen  seconds 
of  longitude  one  second  of  time. 

The  difference  in  longitude  between  any  two  places 
is  the  angular  distance  between  their  meridians,  and 
is  expressed  in  degrees  and  fractions. 

Now  if  we  knew  the  local  time  of  two  places,  we 
could  easily  reduce  this  time  to  degrees  of  longitude 
by  multiplying  the  number  of  hours  by  fifteen,  which 


62      CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

would  give  degrees,  or  by  adding  four  minutes  for 
each  degree. 

On  land  it  is  easy  to  get  simultaneous  times  by 
telegraph,  but  at  sea  this  could  not  be  done,  except  in 
some  instances,  as,  for  instance,  when  the  Atlantic 
cable  was  laid,  the  time  was  transmitted  daily  from 
the  land  to  the  ship. 

Knowing  the  difference  in  time,  and  consequently 
the  longitude,  it  is  easy  to  get  the  distance,  i.  e. , 
taking  into  account  the  number  of  miles  to  a  degree 
on  a  given  parallel.  With  each  degree  of  latitude, 
however,  the  miles  in  a  degree  of  longitude  decrease 
from  the  equator  to  the  pole.  This  is  easily  understood 
by  observing  how  the  meridian  lines  converge  towards 
one  another  at  the  poles,  on  a  globe,  as  we  have  ex- 
plained. 

The  greatest  longitude  a  place  can  have,  east  or 
west,  is  1 80°,  though  sometimes  it  is  reckoned  clear 
around  the  globe  from  a  given  meridian. 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       63 


THE  FINDING  OF  LONGITUDE, 

London  (or  Greenwich)  time  is  the  standard  for 
navigators  all  over  the  world.  It  is  the  universal  time 
meridian.  Every  ship,  therefore,  carries  a  chronom- 
eter, a  finely  made  and  nicely  adjusted  watch,  with  a 
compensation  balance,  hung  and  balanced  so  as  to  be 
affected  as  little  as  possible  by  the  motion  of  the  ship, 
and  this  chronometer  is  set  to 

Greenwich  Mean  Time. 

To  find  his  longitude,  the  navigator  must  know  the 
mean  time  of  the  ship,  and  Greenwich  mean  time. 
This  latter  should  be  kept  by  the  ship's  chronom- 
eter (and  the  error  of  rate  known,  to  be  cor- 
rected in  calculation).  His  own  observations  must 
be  corrected  for  dip  (distance  from  the  sea  level),  re- 
fraction, parallax,  and  also  for  the  semi-diameter  of 
the  sun  (if  he  observes  the  sun).  In  other  words,  the 
navigator  must  know  the  hour  angle  of  the  sun.  In 
order  to  get  this  he  must  know 


64    CURIOSTTIES  OF  LATITUDE  AND  LONGITUDE. 

1.  His  Tatitude. 

2.  The  ?tm's  altitude,  and 

3.  The  sun's  declination  for  that  day. 

And  when  he  has  found  apparent  sun  time,  it  must 
be  corrected  (by  equation)  to  mean  sun  time;  then 
having  found  the  mean  sun  time  of  the  ship,  and 
noted  the  difference  between  it  and  Greenwich  mean 
time,  longitude  is  easily  ascertained  by  converting 
the  difference  in  time  found  into  longitude. 

Latitude  is  taken  at  noon,  when  the  sun  is  near  the 
meridian,  but  longitude  observations  are  taken  morn- 
ing or  evening  when  the  sun  is  a  few  degrees  above 
the  horizon. 

The  instrument  used  is  called  a  sextant,  because  it 
represents  the  sixth  part  of  a  circle. 

If  the  navigator  finds  the  local  time  of  the  ship  to  be 
later  in  the  day,  then  he  is  in  east  longitude.  If  he 
finds  it  to  be  earlier  in  the  day,  he  is  in  west  longitude, 
because  as  the  earth  travels  towards  the  east,  places  to 
the  east  of  us  will  be  later  in  the  day,  while  those  west 
of  us  will  be  earlier  in  the  day.  For  instance, 
if  the  time  of  the  ship  be  noon,  and  the  captain  finds 
that  his  chronometer  says  8  A.  M.,  then  he  is  in  60° 
east  longitude.  But  if  his  chronometer  says  4  p.  M., 
then  he  is  in  60°  west  longitude. 

We  have  shown  how  time  is  kept  by  the  rotation  of 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       65 

the  earth.  Now  the  solar  or  sun  day  is  variable,  but 
bear  in  mind  that  it  is  the  length  of  the  day,  plus  the 
length  of  the  night,  that  makes  the  whole  day. 

The  solar  day  is  variable.  Not  so  the  rotation  of 
the  earth.  That  is  forever  the  same.  It  is  the  mean 
sun,  or  average  sun,  that  makes  the  true  day. 

The  time  as  kept  by  clocks  is  mean  sun  time.  It  is 
the  time  representing  the  24  hours  of  the  earth's  ro- 
tation. 

Sidereal  time  is  time  as  referred  to  the  stars.  A 
sidereal  day,  expressed  in  sidereal  hours,  is  the  same 
as  a  mean  solar  day  expressed  in  mean  solar  hours. 

The  sun  travels  in  the  ecliptic  or  obliquely  across 
the  earth;  if  he  traveled  in  the  equater,  he  would  move 
uniformly,  and  his  path  could  be  divided  into  24 
equal  parts,  but  as  he  moves  obliquely  we  are  obliged 
to  make  an  average  sun  (or  mean  sun).  Apparent, 
or  real  sun  time,  therefore,  is  not  the  same  as  mean  sun 
time.  The  difference  varies  from  o  to  15  minutes. 

In  speaking  of  noon  being  exactly  half  way  be- 
tween sunrise  and  sunset,  we  mean  apparent  noon. 

In  closing  let  me  say  that  a  great  many  cobwebs 
will  be  brushed  away  by  bearing  in  mind  two  facts: 
First,  that  the  earth  rotates  in  exactly  twenty-four 
hours.  Second,  that  it  sweeps  through  the  grand 
circle  of  360°  in  just  that  period.  And  when  we 


66      CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

come  to  understand  that  it  has  done  this  for  ages 
without  appreciable  loss,  we  are  simply  astonished  at 
the  accuracy  of  this  magnificent  clock,  and  the  wis- 
dom that  planned  it. 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       69 

Not  only  would  they  cut  through  cities,  but  streets 
and  even  houses,  so  that  possibly  it  might  be  six 
o'clock  in  the  parlor  and  seven  o'clock  in  the  kitchen 
of  a  house. 

Moreover,  as  Captain  Parker  states  in  his  ' '  Fa- 
miliar Talks  on  Astronomy,"  "standard  time  is 
not  natural,  and  it  would  produce  in  some  instances 
curious  anomalies ;  for  instance,  suppose  standard  time 
was  30  minutes  later  than  real  sun  time  at  a  given 
place.  On  March  2ist  the  sun  would  then  rise  at  6:30 
standard  time,  and  set  at  6:30  standard  time  at  that 
place;  that  would  make  the  morning  5^  hours  long 
and  the  afternoon  6^  hours  long."  Nevertheless,  I 
am  an  advocate  for  a  system  of  universal  standard 
time  for  the  earth,  because  it  is  of  great  benefit  to 
travelers.  And  I  hope  all  the  nations  of  the  earth 
will  soon  adopt  it  for  all  railway  and  steamer  lines. 


70      CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

LONGITUDE. 

The  following  table  gives  the  number  of  miles  in 
a  degree  at  each  parallel  from  the  equator  to  the  pole: 

LENGTH  OF  A  DEGREE  OF  LONGITUDE  AT  EACH 
PARALLEL  OF  LATITUDE. 


STATUTE 

NAUT. 

STATUTE 

NAUT. 

LAT. 

MILE. 

MILE. 

LAT. 

MILE. 

MILE. 

O 

69.160 

60.000 

45 

48.  986 

42.498 

I 

69.150 

59-991 

46 

48.126 

4I-752 

2 

69.119 

59-964 

47 

47-25I 

40.992 

3 

69.066 

59-9I9 

48 

46.362 

40.223 

4 

68.992 

59.855 

49 

45-459 

39-439 

5 

68.898 

59-773 

50 

44.542 

38-643 

6 

68.  783 

59-673 

51 

43.611 

37-835 

7 

68.  647 

59-555 

52 

42.667 

37.016 

8 

68.491 

59-4I9 

53 

41.710 

36.186 

9 

68.314 

59-265 

54 

40.740 

35-344 

10 

68.116 

59-093 

55 

39-758 

34-491 

ii 

67.898 

58.904 

56 

38.763 

33.628 

12 

67.659 

58.697 

57 

37-756 

32.755 

13 

67.400 

58.472 

58 

36.737 

31.872 

H 

67.120 

58.229 

59 

35-707 

30.979 

15 

66.820 

57.968 

60 

34-666 

30.076 

16 

66.499 

57.690 

61 

33-6i5 

29.164 

17 

66.158 

57-394 

62 

32.553 

28.242 

18 

65.797 

57.081 

63 

31.481 

27.311 

19 

65.416 

56.751 

64 

30-399 

26.372 

20 

65-015 

56.404 

65 

29.308 

25-425 

CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       7  I 


STATUTE 

NAUT. 

STATUTE 

NAUT. 

LAT. 

MILE. 

MILE. 

LAT. 

MILE. 

MILE. 

21 

64.594 

56.039 

66 

28.  208 

24.471 

22 

64.154 

55-657 

67 

27.100 

23-509 

23 

63-695 

55.258 

68 

25-983 

22.540 

24 

63.216 

54-843 

69 

24-857 

21.564 

25 

62.718 

54'4H 

70 

23.723 

20.582 

26 

62.201 

53-962 

7i 

22.582 

19-593 

27 

61.665 

53-497 

72 

21-435 

18.598 

28 

61.  no 

53-oi6 

73 

20.282 

17-597 

29 

60.536 

52.518 

74 

19.122 

16.590 

30 

59-944 

52.005 

75 

!7-956 

I5-578 

31 

59-334 

5*-476 

76 

16.784 

14.561 

32 

58.706 

50-931 

77 

15.607 

13-539 

33 

58.060 

50-370 

78 

14.425 

12.513 

34 

57-396 

49-794 

79 

13-238 

11.484 

35 

56.715 

49-203 

80 

12.047 

10.452 

36 

56.016 

48.597 

81 

10.853 

9.417 

37 

55-  3°° 

47.976 

82 

9-656 

8-379 

38 

54-568 

47-340 

83 

8.456 

7-338 

39 

53-8l9 

46.690 

84 

7-253 

6.294 

40 

53-053 

46.026 

85 

6.048 

5.248 

4i 

52.271 

45-348 

86 

4.841 

4-200 

42 

51-473 

44-656 

87 

3-632 

3-!5i 

43 

50-659 

43-950 

88 

2.422 

2.  101 

44 

49.830 

43-231 

89 

1.  211 

1.050 

72      CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 


LATITUDE. 

The  earth  is  an  oblate  spheroid,  i.  e. ,  its  Polar 
diameter  is  about  26^/2  miles  shorter  than  its  Equa- 
torial diameter. 

Were  the  earth  a  perfect  sphere,  the  miles  in  a 
degree  of  latitude  would  be  the  same  at  each  parallel. 
They  do  not  vary  much,  however,  as  the  following 
table  will  show: 

LENGTH  OF  A  DEGREE  OF  LATITUDE  AT  EACH 
PARALLEL. 


STATUTE 

NAUT. 

LAT. 

MILE. 

MILE. 

O 

68.698 

59.600 

I 

68.698 

59.600 

2 

68.699 

59.601 

3 

68.700 

59.602 

4 

68.  702 

59-603 

5 

68.  704 

59-605 

6 

68.706 

59.607 

7 

68.  709 

59.609 

8 

68.712 

59.612 

9 

68.715 

59-6I5 

10 

68.719 

59.618 

ii 

68.723 

59.621 

12 

68.728 

59-625 

J3 

68-733 

59.629 

14 

68.738 

59-634 

15 

68.744 

59-639 

STATUTE 

NAUT. 

LAT. 

MILE. 

MILE. 

45 

69.044 

59-899 

46 

69.056 

59.910 

47 

69.068 

59.920 

48 

69.  080 

59-931 

49 

69.092 

59-941 

50 

69.104 

59-951 

5i 

69.116 

59.962 

52 

69.128 

59-972 

53 

69.  140 

59.982 

54 

69.151 

59-992 

55 

69.162 

60.002 

56 

69.173 

6O.OI2 

57 

69.184 

60.022 

58 

69.  195 

60.032 

59 

69.206 

60.041 

60 

69.217 

60.050 

CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       73 


STATUTE 

NAUT. 

LAT. 

MILE. 

MILE. 

16 

68.750 

59-645 

17 

68-757 

59-65I 

18 

68.764 

59-657 

19 

68.771 

20 

68.779 

59.669 

21 

68.787 

59.676 

22 

68.795 

59-683 

23 

68.804 

59.691 

24 

68.813 

59.699 

25 

68.822 

59-707 

26 

68.831 

27 

68.840 

59-723 

28 

68.850 

59-731 

29 

68.860 

59-740 

3° 

68.870 

59-749 

31 

68.881 

59-758 

32 

68.  892 

59-767 

33 

68.903 

59-776 

34 

68.914 

59.786 

35 

68.925 

59-796 

36 

68.936 

59.806 

37 

68.947 

59.816 

38 

68.959 

59.826 

39 

68.971 

59-836 

40 

68.983 

59.846 

41 

68.995 

59.856 

42 

69.  007 

59.866 

43 

69.019 

59-877 

44 

69.031 

59.888 

STATUTE 

NAUT. 

LAT 

.  MILE. 

MILE. 

6l 

69.228 

60.059 

62 

69.238 

60.068 

63 

69.248 

60.077 

64 

69.258 

60.086 

65 

69.268 

60.  094 

66 

69.277 

60.  102 

67 

69.286 

60.  no 

68 

69.294 

60.117 

69 

69.302 

60.124 

70 

69.310 

60.131 

71 

69.318 

60.137 

72 

69.326 

60.  143 

73 

69-333 

60.  149 

74 

69-339 

60.155 

75 

69-345 

60.  161 

76 

69-35I 

60.166 

77 

69-357 

60.171 

78 

69.362 

60.175 

79 

69.367 

60.179 

80 

69.371 

60.183 

81 

69-375 

60.186 

82 

69.378 

60.189 

83 

69.381 

60.192 

84 

69.384 

60.194 

85 

69.387 

60.196 

86 

69.389 

60.  198 

87 

69.390 

60.  199 

88 

69.391 

60.  200 

89 

69.392 

60.201 

74      CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 

To  convert  nautical  miles  into  statute  miles, 
multiply  nautical  miles  by  1.15266. 

To  convert  statute  miles  into  nautical  miles,  divide 
statute  miles  by  1.15266. 

A  nautical  or  sea  mile  is  the  length  of  a  minute  of 
longitude  at  the  equator  at  the  level  of  the  sea. 

The  circumference  of  the  earth  contains  131,459,- 
328  feet  •*-  360°  X  60  =  length  of  a  knot  =  6086.  + 
feet. 

The  value  of  a  degree  of  longitude  at  the  equator 
is  60  geographical  or  69^  English  miles.  To  ascer- 
tain the  distance  between  any  two  places  on  a  globe 
or  map  on  a  globular  projection,  take  the  distance 
between  the  two  places  with  a  thread  or  the  edge 
of  a  piece  of  paper,  apply  this  to  the  equator,  and 
get  the  exact  number  of  degrees,  then  multiply  by 
60  or  69*^,  as  the  case  may  be. 

ANGULAR  MEASUREMENT. 
60"  =  i'. 
60'  =  i°. 
30°  =  i  Sign. 
90°  =  i  Quadrant. 
4  Quadrants,  or  360°  =  i  Circle. 

To  CONVERT  LONGITUDE  INTO  TIME, 
divide  degrees,  minutes  and  seconds  by  15,  or  mul- 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       75 

tiply  by    4  and  the  result  will  be  in  minutes  and 
fractions  of  a  minute.     For  example: 

86°  -  24'  -  30" 

4 
60)  349mjand  f| 

5    49    38 

To  CONVERT  TIME  INTO  LONGITUDE, 
multiply  by  15,  or  divide  the  time  reduced  to  minutes 
by  4.     For  example:      5h  -  49™  38s  =  349m  and  ff 
•*  4  -87°  -24'  -30". 


76      CURIOSITIES  OF  LATITUDE  AND  LONGITUDE. 


CURIOSITIES  OF  LATITUDE  AND  LONGITUDE.       77 


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80      CURIOSITIES  OF  LATITUDE   AND  LONGITUDE. 


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QB    Cowell-LAtitude  and  Longitude. 

631 

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